import java.util.*

data class Context(val sum: Int, val coins: List<Int>)

fun coins(amount: Int, coins: List<Int>): List<Int> {
    val sorted = coins.distinct().sortedDescending()
    val initialContext = Context(0, listOf())
    val queue = ArrayDeque<Context>()
    queue.offer(initialContext)
    while (queue.isNotEmpty()) {
        val context = queue.poll()
        if (context.sum == amount) {
            return context.coins
        }
        sorted.asSequence()
            .filter { context.coins.isEmpty() || it <= context.coins.last() }
            .filter { context.sum + it <= amount }
            .forEach { queue.offer(Context(context.sum + it, context.coins + it)) }
    }
    return listOf()
}

fun main() {
    val coins = coins(76, listOf(1, 3, 4, 10))
    println(coins)
}